To find the possible values of angle X, we can use the Law of Cosines. The Law of Cosines states that in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle opposite the first side.
Using the Law of Cosines, we can write the following equation for triangle VWX:
V^2 = W^2 + X^2 - 2WXcos(W)
Plugging in the given values, we have:
V^2 = (8.8)^2 + X^2 - 2(8.8)(X)cos(85°)
V^2 = 77.44 + X^2 - 15.36X
Solving for X, we can use the quadratic formula:
X = (-(-15.36) ± √((-15.36)^2 - 4(77.44)(1)))/2(1)
X = (15.36 ± √(234.84))/2
So the possible values of X are approximately:
X = (15.36 + 15.32)/2 = 15.34 inches
X = (15.36 - 15.32)/2 = 0.02 inches
Converting the length of X to degrees, we can use the inverse cosine function (arccos) to find the angles:
∠X = arccos(X/V)
For the first value of X (15.34 inches), we have:
∠X = arccos(15.34/V)
Since V is not given, we cannot determine a numerical value for ∠X, but it is safe to say that it will be between 0° and 90°.
For the second value of X (0.02 inches), we have:
∠X = arccos(0.02/V)
Since X/V is very close to 0, the cosine value will be close to 1, so the angle will be close to 0°. To the nearest 10th of a degree, ∠X = 0°.